"I swear to be faithful to the republic and loyally respect its constitution," Mr Napolitano, 80, said before a joint gathering of both houses of parliament.
Italy's new head of state then delivered his inaugural address to the nation, urging that the transfer of power following Italy's bitterly fought general election last month be handled with "respect" and "mutual recognition".
"It is with deep feeling that I come before this assembly, where I have spent a large part of my political life, and where I learned the supreme importance of parliamentary institutions," said Mr Napolitano, who wore a navy blue suit and a blue and white tie for the occasion.
"The time has now come for Italy to hand over political power," he said, calling for "respect, mutual recognition and attentiveness to differing viewpoints" and "a confrontation worthy of the parliament".
"Constitutional unity is the basis for national unity," said Napolitano, a committed European, adding that there was "no alternative to the relaunch of the process of the European constitution".
Mr Napolitano also paid tribute to his predecessor, describing the 85-year-old Mr Ciampi's seven-year reign as "exemplary", a comment that won lengthy applause from the gathered parliamentarians.
On Italy's troubled economy, he said he wanted to give a "confident message", adding that Italy needed "more justice and social cohesion".
Mr Napolitano takes over as president after winning the backing of Mr Prodi's centre-left alliance in a vote by lawmakers last week that underlined the country's political divisions.
As president he will enjoy the splendour of the Quirinale Palace perched atop one of Rome's seven hills.
His first important task will be to name Mr Prodi as prime minister, enabling the professorial former European Commission president to install a new government after five years of conservative administration under the flamboyant, and often controversial, Silvio Berlusconi.
Mr Napolitano is expected to name Mr Prodi on Wednesday after a formal round of talks on Tuesday with leaders of all Italy's political parties.